Yes, you can apply for H4 extension and H4 EAD too…Make sure to submit all previous receipt notices to confirm, you are maintaining status.
you would submit your proof of status and COS receipt notice. Also, include a letter stating that you are waiting for the COS approval, but in the meantime, you are applying this as your spouse H1B is extended.
Your fastest option is to get your spouse h1B approved in premium, you leave the country, get stamping done and re-enter.
My spouse’s H1-B visa based on which I filed for COS, would have already expired by the time my COS would be processed. Would that be a problem in the processing of extension?
No, it will not. That’s the reason, you are submitting that your spouse is filing extension and you are also waiting for the processing… Talk to your attorney on this.